Racing bikes are either silver or blue. Every silver bike is
a racing model. 1/2 of the blue bikes are racing models. 1/3 of the
bikes are racing models. There are 40 blue bikes and 30 silver
bikes. How many bicycles are neither blue nor silver?

I am having a hard time changing a word problem into a formula in
order to get the results. For example: Apples cost $1.50 per pound
and pears cost $2.30 per pound. A total of 8 pounds of apples and
pears were bought, and the price was $14.00. How many pounds of pears
were bought?

A water main is being laid using pipe that comes in either 18-foot or
20-foot sections. The water main will require 14 fewer sections of 20-
foot pipe than if 18-foot sections are used. Find the total length of
the water main.

An advertisement for an orange drink claims that the drink contains 10%
orange juice. How much pure orange juice would have to be added to 5
quarts of the drink to obtain a mixture containing 40% orange juice?

A student struggles with a word problem that asks for specific sums of counting
numbers. Three different doctors weigh in with increasingly sophisticated and
comprehensive problem-solving approaches: programming spreadsheet formulas;
applying combinatorics; and invoking quadratic Diophantine and Pell equations.

A woman sells half of her eggs and half an egg to Peter. Later, she sells
half her eggs again and half an egg to John, and so on with more people.
Finally the woman is left with only one egg. How many eggs did she start
with?